Girls: 81
boys: 75
4x +6 = 156
4x = 150
x = 37.5
2x = 75
girls: 75 + 6
boys: x
We know that the building must form a right angle with the ground, so the triangle formed by the ladder, the wall, and the distance between the base of the ladder and the wall is a right triangle. We can use the Pythagorean theorem to find the distance the ladder is from the building.
a^2 + b^2 = c^2
We know that the ladder is the hypotenuse because it is opposite the right angle.
a^2 + b^2 = 20^2
Substitute the length of the other side and solve.
a^2 + 17^2 = 20^2
a^2 + 289 = 400
a^2 = 111
The distance from the wall to the bottom of the ladder is the square root of 111 or approximately 10.5357 feet
Here are a few things you'll need to know for this question:
- Domain: <u>The list of x-values that are possible on a line.</u>
- Range: <u>The list of y-values that are possible on a line.</u>
- Interval Notation: <u>Shows the domain/range using the endpoints</u>. Brackets mean that the endpoint is included, parentheses mean the endpoint is excluded. Ex: (2,10]. 2 is excluded, 10 is included.
- Closed Circles: <u>The endpoint is included.</u>
- Open Circles: <u>The endpoint is excluded.</u>
So firstly, let's look at the domain. We see that there is a closed circle at x = -2 and an open circle at x = 5. Using what we know, <u>the interval notation of the domain is [-2,5).</u>
Next, let's look at the range. We see that there is a closed circle at y = -5 and an open circle at y = 2. Using what we know, <u>the interval notation of the range is [-5,2).</u>
Lemme think real quick...
